In the B-model, the Yukawa coupling is related to a generalization of Kaneko and Zagier's theory of quasi-modular forms developed by Movasati in [1]}. His approach relies on the algebraic de Rham cohomology (see [2]}) and on the Gauss-Manin connection (see [3]}). The idea is to consider the moduli space \(\sf T_{\rm cl}\)  of pairs \((W,[\alpha _1,\dots ,\alpha _4])\) , where \(W\)  is a mirror quintic and \([\alpha _1,\dots ,\alpha _4]\)  is a basis to the third de Rham cohomology of \(W\)  that, in some sense, respects the Hodge filtration. After computing the Gauss-Manin connection matrix, he was able to define a differential algebra attached to \(\sf T_{\rm cl}\)  with elements that behave similarly to modular forms: he found relations between the generators and their derivatives which generalizes the Ramanujan relations we have for the Eisenstein series. The procedure described above is part of a more general program known as Gauss-Manin connection in disguise (GMCD, for short). It is an attempt to construct a general theory of modular forms via functions on a moduli space submitted to a differential equation. Some cases have already been treated, from the elliptic curve case (see [4]}) to more general cases as in [5]} and the more recent paper [6]}.
